Many people will give you reasons for their “adding to” taiji, and yes, they make sense! If you look another way, thought, it will also make sense.
Grandmaster Hong Junsheng only learned and practiced Wu Style Taijiquan for about half a year prior to Chen Style. The rest of his life, no one ever saw him do anything related to Wu Style, except the fact that he acknowledged the Wu Style when talked about and wrote about Taiji. His taiji curriculum and life involved only Jibengong and forms (mostly Yilu). Nobody ever saw him holding a sword. And yet, the level of mastery of taiji and his health reached a a point unparalleled.
So anyway you want to approach taiji, you will find support for your reasons, it is totally up to you. But I guarantee you, how you choose to do it will bear totally different results.

Master Chen, is it fair to say that even for a an individual who is relatively small, the practice of taiji is enough to achieve strength. Do you advocate the use of other tools for strengthening? Thank you!

Yes, definitely. Anyone is born with enough prerequisite to be capable of using taiji to get self-defense skills. I don’t advocate using anything other than within the taiji curriculum, i.e. form training, sword, broadsword, staff, etc.

I can vouch for that! Being a typical southerner I am more on the athletically petit side. The battle is less on getting the movements right, but having the courage to use my skills in a David versus Goliath situation. Taiji is the only martial art that would allow me to see and put to practice that I have a chance with bigger opponents. It is especially encouraging that I had learned that one of the principles in Taiji is to “be small”. I had the opportunity to test this principle in a recent push hand exchange, and I truly felt that the fear factor is being conquered by higher and more accurate skill.

For your reference, I have studied many martial arts from Wing Chun (again typical of southerners) to Cha Quan.

In the past, I did a lot of warm up exercises before doing taiji. Now I only do a few such as the waist, kua and knees. My question is whether there is a need to enhance movement such as stretching the legs and doing the splits, or we don’t need these at all? If I cannot do the splits will I still gain higher level taiji skills? I feel that in the routines, every move is designed to stretch the ligaments and the arms are to stretch as much as possible. I feel that the entire routine is to stretch the arms again and again till they feel strong.

The real question you are asking is: “What are we training in Taiji?” One of the most important things (though not publicly expressed) we learn in taiji is to foster new habits that are taiji based in our movements. A quote from Grandmaster Hong Junsheng is “When you follow the rules to the extreme, every thing you do is automatically a form in the routine.” The routines encompass warm ups, basic foundations, technique and internal energy!
Yes you are right, doing the routine will make you stretch everything in your body. You can also do specialized training. For example, if you want to stretch your legs in order to do the split, you can practice the form “Fall into a Split” repeatedly.